Neither Rex nor Rick have any innate powers (though it was theorized once that their powers derive from a metagene, like most DC superheroes). Any superhuman abilities they display are derived from the use of Miraclo. Taking Miraclo grants a user several abilities for the span of an hour. Most obvious are the superhuman strength, durability, increased resistance to physical damage (to the extent of being impervious to small arms fire) and speed enhancements. Other, lesser known and mentioned powers include night vision and the ability to survive underwater. Rex and Rick both took Miraclo in pill form, but Rick currently uses a transdermal patch.
The amount of Miraclo that can be taken per day has varied. Normally, it is once a day, but in some instances, Rex has been shown taking another pill as soon as an "Hour of Power" runs out. Miraclo works specifically on the Tylers and may or may not work on others who take it. In one instance it worked on an animal, Dr. Mid-Nite's owl, Hootie as well as the villain Bane.
Rex and Rick both wore an hourglass around their necks given to them by the Hourman Android. It was filled with energized tachyons, time in its most basic form. It gives Rick "time vision," flashes of events that will happen exactly one hour later as well as the ability to touch those out of phase with normal time. The latter effect comes to anyone holding the hourglass. Rex displayed neither of these abilities.
"Tyler" is often simply called an android, but is actually an intelligent machine colony (possibly a form of nanotechnology) created by Tylerco in the far future. If damaged, this colony can effortlessly multiply and repair. His software is encoded with the genetics of Rex Tyler, giving him all of Rex's memories. He originally possessed the Worlogog, which gave him complete control over time. He later gave all but a shard of it up, but not before he absorbed all of Batman's memories of the JLA.
Though not as powerful as he was originally, Tyler still retained super strength, durability, and speed equivalent to a person using Miraclo. He was able to access an "Hour of Power," sixty minutes during which he had power over time. He can do many things with this control: move between picoseconds, travel though time, use his own time vision (which allows him to see a person's past and future as well as age) or make people and things younger, slow a person down until essentially frozen, create tunnels between different time periods, and share power with other individuals (though the amount of time that he provides them power for directly takes away from his sixty minutes). Tyler activates the Hour of Power at will and the hourglass on his chest keeps count of the time. There seems to be some doubt how often he can use his Hour of Power. Like the other Hourmans' use of Miraclo, sometimes Tyler is said to only have one Hour of Power a day, while at other times he simply must wait another hour to recharge before he can reactivate.
Tyler also has a timeship that he can summon from the timestream. It is connected to him and reacts to his thoughts. It normally appears as a Viking-style wooden sailing ship adorned with clocks, but it can change form as Tyler dictates to anything from a simple wooden skiff to a futuristic spaceship and also be used as a weapon, as when Hourman made a large hand out of it to trap Extant. The ship can travel through time, to alternate timelines, or through hypertime.